High flow rates through catheters are necessary to maximize the efficiency of medical procedures such as dialysis and the introduction of contrast in so-called “power injection” procedures. Certain catheter designs have been developed to increase flow rates, such as in U.S. Pat. Nos. 7,410,602, 6,595,966, and 6,230,423, each of which is incorporated herein by reference, but there remains a growing need for catheters that can accommodate increased flow rates. There is also a need for very small diameter catheters for positioning in smaller bodily lumens, yet allowing for high flow rates and requiring high mechanical strength.